Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | D3×C22⋊C16 |
| Fitting | C3×C22⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,4)(21,22,23);(1,2)(3,4)(5,6,7,10,8,11,13,16,9,12,14,17,15,18,19,20);(22,23)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1314, #10704250, D3×#1315, … |
| maximal normal subgroup of | D3×#1314, #10704250, D3×#1315, … |
| maximal quotient of | D3×#1314, D3×#1322, #10704382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1681);